Construct Smallest Number From DI String

Problem Statement

You are given a string pattern consisting of the characters:

• 'I' (Increasing): The next digit must be greater than the current one.
• 'D' (Decreasing): The next digit must be smaller than the current one.

Your task is to generate the smallest lexicographical number using digits 1-9 (without repetition) that follows this pattern.

Example 1

Input:
pattern = "IDID"

Output:
13254

Explanation:

• 1 < 3 (I)
• 3 > 2 (D)
• 2 < 5 (I)
• 5 > 4 (D)

Other possible numbers are "14253" and "15234", but "13254" is the smallest.

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Example 2

Input:
pattern = "DDD"

Output:
4321

Explanation:

• 4 > 3 (D)
• 3 > 2 (D)
• 2 > 1 (D)

Other possible numbers like "9876" or "7654" are larger.

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Constraints

• 1 <= pattern.length <= 8
• pattern consists only of 'I' and 'D'.